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Branching processes, trees and the Boltzmann equation

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  • Chauvin, Brigitte

Abstract

Using the formalism of random trees, we construct a process solution of the spacehomogeneous Boltzmann equation. We deduce a simulation method having relationships with both the Nanbu's method and with Bird's method. The efficiency is clear for the Kac's caricature and some scalar Boltzmann cases because the algorithm is then explicit. This construction is also the tool for proving a geometric convergence to the equilibrium.

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  • Chauvin, Brigitte, 1995. "Branching processes, trees and the Boltzmann equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 38(1), pages 135-141.
    • Handle: RePEc:eee:matcom:v:38:y:1995:i:1:p:135-141
    DOI: 10.1016/0378-4754(93)E0076-H
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    Cited by:

    1. Fournier Nicolas & Giet Jean-Sébastien, 2004. "Exact simulation of nonlinear coagulation processes," Monte Carlo Methods and Applications, De Gruyter, vol. 10(2), pages 95-106, June.
    2. PARESCHI Lorenzo & WENNBERG Bernt, 2001. "A recursive Monte Carlo method for the Boltzmann equation in the Maxwellian case," Monte Carlo Methods and Applications, De Gruyter, vol. 7(3-4), pages 349-358, December.

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